Luminosity Classes
Class Description Examples
Ia Bright Supergiants Deneb (A2Ia)
Ib Supergiants Antares (M1Ib)
II Bright Giants Canopus (F0II)
III Giants Capella (G5III)
IV Subgiants Beta Cru (B0IV)
V Main Sequence Vega (A0V)

Luminosity Classes

Luminosity classes correspond to horizontal and diagonal bands on the HR diagram that are related to the size of a star. This somewhat qualitative classification is exhibited in the adjacent table and in the HR diagram displayed below.

Classification
Luminosity classes are labeled with Roman numerals from I to V: I are supergiant stars, II are bright giants, III are ordinary giants, IV are subgiants, and V are ordinary main sequence stars. The complete spectral classification for a star is then given by specifying both the spectral class and the luminosity class. For example, the nearby star alpha Centauri is classified as a G2V star, meaning that it is a main sequence (V) star of spectral class G2 (intermediate between G and K but closer to G in the spectral sequence).

More Detailed Classification
Luminosity classes are sometimes subdivided. For example, classes Ia and Ib are bright supergiants and less bright supergiants, respectively. Intermediate labels such as IV-V for a very luminous main-sequence star are sometimes used. For example, the star Altair is classified as A7IV-V. This means that its spectral class is A7 and its luminosity class is intermediate between main sequence (V) and subgiant (IV).

Luminosities within Classes
The luminosities within the giant and supergiant classes are relatively constant as a function of spectral class (they consist of almost horizontal lines on the HR diagram). However, note that luminosity class V (main sequence stars) covers a very large range of absolute brightness, since blue main sequence stars are much brighter than red main sequence stars. The luminosity of white dwarfs also depends rather strongly on spectral class.

A G2V Main Sequence Star

Since our Sun is a star, we can classify it according to its spectral and luminosity classes. The Sun is an example of a main sequence star, of spectroscopic type G2. Therefore, the combined color and luminosity class for the Sun is G2V (the same as alpha Centauri).

Technically Speaking: Luminosity, Temperature, and Radius

If we assume stars to be spherical blackbody radiators, we can often infer their sizes from their luminosities. From the Stefan-Boltzmann law, the total luminosity (energy emitted per second from the surface of the star) is given by multiplying the energy emitted from each square meter of the surface per second by the total number of square meters on the surface:

L = luminosity = constant x surface area x (temperature)4 = 4πaR2T4

where a is a constant and π = 3.1416, T is the temperature, and R is the radius of the star. Thus, the ratio of the luminosities for two stars (labeled by 1 and 2) is

L1 / L2 = ( 4πaR12T14) / (4πaR22T24)

Cancelling like factors and rearranging, we have

L1 / L2 = (T1 / T2)4 x (R1 / R2)2

or equivalently we can solve for the ratio of the radii:

R1 / R2 = (T2 / T1)2 x (L1 / L2)1/2

This can be put in a particularly simple form if we choose the Sun to be star 2 and agree to measure all surface temperatures, radii, and luminosities in units of that for the Sun. Then we can set all quantities with subscript "2" numerically equal to one (and drop the no longer necessary subscript "1") to give

R = L1/2 / T2

where T is the surface temperature, L the luminosity, and R the radius of the star in question, all expressed in solar units. The utility of this last expression is that we can often estimate T for a star from its spectrum and measure its luminosity L. This then allows us to calculate the radius if we assume that the star is a spherical blackbody. For example, let's estimate the radius of the A0V star Vega, which is 51 times more luminous than the Sun. The surface temperature of an A0V star is about 10,000 K and that of the Sun is about 5800 K. Therefore

R = L1/2 / T2 = (51)1/2 / (10,000 / 5800)2 = 2.4 solar radii

If Vega and the Sun are reasonably good blackbodies (highly likely), we conclude that Vega must be 2.4 times larger than the Sun to account for its brightness.